## _wp15224

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---

### I. Introduction — problem and proposed transitional approach
- Zero lower bound (ZLB) arises because government-issued paper currency guarantees a zero nominal interest rate obtainable in unlimited quantities, creating an interest-rate floor that hinders negative nominal policy rates.
- Proposal: a transitional electronic money system in which electronic money is the unit of account while paper currency remains in circulation, combined with a time-varying paper currency deposit fee levied at the central bank’s cash window, can eliminate the option to circumvent negative rates by withdrawing, storing, and redepositing paper currency.
- Key operational point: levy the paper currency deposit fee on net deposits at the cash window to create a time-varying exchange rate between electronic money and paper currency so paper currency can be caused to depreciate relative to electronic money when needed.
- Political/practical advantages:
  - No need for extra regulations or quantity constraints; policy works through prices.
  - Can be implemented at the central bank’s cash window within weeks.
  - Serves as a transitional system complementary to a long-run move toward a cashless economy.

### II. Mechanism: time-varying deposit fee and preventing arbitrage
- Three attack points to prevent arbitrage against negative rates:
  - Attack withdrawals (restrict or fee withdrawals): disadvantages include impairing spending, destroying option value, anticipatory hoarding, and political difficulty.
  - Attack storage (tax/prohibit storage): hard to enforce because low-tech secret storage is feasible, risking disintermediation.
  - Attack redeposit (time-varying deposit fee at central bank cash window): preferred in this paper.
- Mechanics of the time-varying deposit fee:
  - Fee levied only at the cash window when private banks deposit paper currency; no new rules for bank–customer interactions required.
  - Fee on net deposits makes the bank’s effective receipt for one paper dollar equal to (1 - deposit fee) electronic dollars (ignoring transaction costs).
  - Charging the fee on net deposits makes the exchange rate two-way (discount on withdrawals and deposits), avoids banks reorganizing cash flows to net out before interacting with the cash window, and establishes a clearly defined crawling peg for the exchange rate.
- Retail pass-through considerations:
  - Retailers often accept different payment types at face value despite differing net receipts (example: credit card net receipts of 96 or 97 cents on the dollar), so retailers may similarly treat discounted cash as if at par unless discounts exceed retailers’ cost differences.
  - Up to a deposit fee of several percent, retail behavior may not change and could further encourage treating cash and card payments at par.
  - Research agenda: map retailer cash-handling costs and contractual card fees to determine when and where exchange-rate discounts would be passed through at retail.

### III. The paper currency interest rate (PCIR) and exchange rate dynamics
- Definitions and operationalization:
  - Electronic money is the numeraire; define X = number of electronic dollars per paper dollar. The PCIR is the rate of change in X: (dX/dt)/X = PCIR.
  - Monetary policy committees would add a fourth interest-rate choice: the paper currency interest rate (PCIR), alongside target rate, interest on reserves, and lending rate.
  - The deposit fee’s time path (its rate of change) is the operational instrument that creates the desired PCIR.
- Time-path scenarios for returning paper currency to par:
  - Swift Return to Par:
    - Rapid return to par creates a high appreciation (high PCIR) and can create a new, higher effective lower bound; anticipation would encourage preemptive paper-currency storage.
    - Considered a serious policy mistake.
  - Gradual Return to Par:
    - Keep PCIR equal to the target rate (plus/minus a small spread) until parity is reached, then set PCIR = 0.
    - Returns exchange rate to par as fast as consistent with keeping the ZLB non-binding; small spreads limit shoe-leather costs.
  - Friedman Rule:
    - Keep PCIR equal to the target rate at all times (plus/minus a small spread).
    - Implies paper currency can go above par if long-run average nominal rate is positive; consistent with achieving zero inflation in the electronic unit of account without forcing deflation in that unit.
  - Seignorage without Inflation (Never Return to Par):
    - Constantly depreciate paper currency to extract seignorage while maintaining low/zero inflation in the electronic unit of account.
    - Example: central bank sets a constant PCIR equal to -4 percent; paper money value continues to fall relative to electronic money without creating inflation in the electronic unit of account.
- Policy commitment required:
  - Keep PCIR at most a small spread above the target rate and interest on reserves (spread smaller than physical storage cost) to avoid incentives for storage during policy normalization.
  - Commitment to the exchange rate one day ahead plus this PCIR behavior suffices to make negative-rate policy function smoothly.

### IV. Absence of arbitrage and numerical illustration
- No-arbitrage condition:
  - Absent storage costs, absence of arbitrage requires the PCIR to be essentially equal to other short-term safe rates (interest on reserves, repo, short-term bill rates).
  - Time-varying X serves like a “sundial” tracking cumulative electronic-account interest earned; the rate of change in the deposit fee (not its level) ensures parity of returns across paper and electronic holdings over time.
- Numerical/example context:
  - Example trajectory: other short-term rates = -2 percent during 2009–2010, 0 percent during 2011, and +2 percent thereafter; setting PCIR equal to these short-term rates prevents arbitrage across 2009–2014.
  - Example illustration: $100 deposited in an electronic short-rate account on January 1, 2009 becomes $98, $96, $96, $98, $100, and $102 on successive New Year’s Days; paper-currency storage, converted using X, can be made to match this path through 2014 when PCIR is set accordingly.

### V. Pass-through of negative interest rates and behavioral evidence
- Empirical and behavioral expectations:
  - Experience from Switzerland, Sweden, Denmark, and the eurozone (2014–15) shows negative policy rates are not immediately fully passed through to typical small household accounts.
  - Banks likely distinguish legacy customers (shield from modest negative rates) from hot-money customers (pass negative rates through).
  - Large deposits from firms and institutional investors are more likely to pay negative rates.
- Central bank strategic advantage:
  - Acting indirectly via private-firm decisions can blunt political backlash while retaining transmission.
  - Blunted pass-through at retail is not fatal because primary transmission channels for negative rates are via asset prices, exchange rates, and purchases of investment goods and durables (usually paid electronically).
- Evidence cited:
  - Danmarks Nationalbank: its certificate-of-deposit rate has been -0.75 percent since Feb 6, 2015; negative rates did not weaken pass-through to money market rates; deposit/lending rates for households were not fully passed through, while large deposits paid negative rates; no substantial change in currency-in-circulation usage at current rates.

### VI. Impacts on financial sector, contracts, and spreads
- Impact on banks and spreads:
  - The spread between other short-term rates and PCIR matters for bank profitability; in current systems negative short-term rates combined with a zero paper-currency rate compress spreads and hurt profitability.
  - Electronic money system makes that spread a policy variable and can avoid compressing bank spreads unduly because depreciation mechanism still gives depositors incentive to keep funds in banks even if deposit rates are negative.
  - Banks’ customer-relations choices (shielding small accounts) may reduce pass-through and affect profits; central banks can subsidize banks to shield small accounts by linking above-market zero interest ceilings on reserve accounts to banks’ behavior in shielding households while passing negative rates to other depositors.
- Possible spread paths (target rate minus PCIR):
  - Case 1 (Swift Return to Par): spread may not always be positive.
  - Cases 2–4 (Gradual, Friedman, Seignorage): spread remains positive at all times in the illustrations.
  - A policy of a fixed small positive spread (e.g., a constant small spread below the target rate except when it would take paper currency above par) provides predictable communication and minimizes political salience.
- Impact on debt contracts:
  - When paper currency is below par, borrowers might have an option to repay in cheaper paper currency unless contracts specify the unit of payment.
  - Remedies:
    - Legislate that debt contracts refer to units of electronic (bank) money.
    - Include contractual clauses specifying treatment when paper currency is away from par (legal precedent: enforceability of gold clauses suggests electronic-money clauses are enforceable).

### VII. Costs, benefits, psychological and computational considerations
- Primary benefits of breaking the ZLB:
  - Removes constraint on how low nominal interest rates can go, expanding monetary policy tools for stabilization.
  - Allows lower long-run inflation targets without sacrificing stabilization.
- Psychological and computational costs of paper currency away from par:
  - Example: a 0.5 percent fall in the value of paper currency with a corresponding fall in the exchange rate from 1 to .995 over the course of a year.
  - Typical households may not fully perceive such a 0.5 percent depreciation because retail prices they face likely will not reflect it.
  - Displacement of paper currency from the center creates attachment-related queasiness; mitigants include fostering attachment to the electronic unit.
  - Businesses can handle a non-par exchange rate relatively easily; households facing surcharges face complexity akin to U.S. sales taxes.
- Additional practical costs:
  - Unintentional distortion of preexisting debt contracts.
  - Additional transactions costs from physical transportation of paper currency if below-par cash is accepted at face value.
- Legal/contractual mitigants:
  - (1) Law interpreting monetary amounts in contracts as referring to electronic money or equivalent at current exchange rate.
  - (2) Boilerplate clauses in debt contracts specifying assessment when paper currency is away from par.
- Benefit: taxing paper currency without inflation
  - Ability to tax paper currency separately from the inflation target of the unit of account.
  - Use cases: combating criminal activity or tax evasion associated with paper currency; experimenting toward a fully cashless economy.

### VIII. Dynamic considerations, model dependence, and financial stability
- Distinction: temporary vs. chronic low interest rates.
- If markets believe ZLB has been broken and central banks will use negative rates to close output gaps, markets will anticipate higher future interest rates appropriate to a non-depressed economy.
- Model dependence:
  - In models where monetary policy affects activity, adding policy tools is unambiguously good if central bank judicious.
  - In models with investment adjustment lags and Q-theory smoothing, an initial interest cut can lead to different subsequent long-run interest rates once activity adjusts; interest cuts might therefore raise post-adjustment interest rates.
- Financial stability:
  - Low long-run rates might raise fundamental present values and potentially increase divergence from fundamentals, but if negative rates lead ultimately to higher long-run rates, they could dampen this instability channel.
  - Important to pair negative interest rates with progressively higher equity (capital) requirements (e.g., high capital conservation buffers).
- Edge-case tradeoffs:
  - If low long-run rates are beneficial (e.g., to maintain solvency for high-debt countries), negative short-term rates could be counterproductive by inducing a boom that raises long-run rates.

### IX. What it takes to break through the ZLB: essential elements and policy levers
- Core claim: a specific policy can break through the ZLB; essential vs. non-essential elements identified.
- If the government has trouble establishing electronic money as the unit of account:
  - Governments can influence units of account via tax rules, accounting standards, and court-adjudicated contract interpretation.
  - Central bank can make electronic accounts offer a significantly higher rate of return than paper currency to reward holding electronic balances and induce shift of unit-of-account usage.
  - Example “peso-to-zero” illustration: appreciate electronic peso relative to paper peso at close to 7 percent per year while staying at natural output, then anchor electronic peso inflation near zero to shift pricing and contracting.
- Avoiding “paperization”:
  - Risk: prolonged zero or negative target rates with paper currency at par can encourage greater use of paper currency.
  - Central bank can choose a large enough spread between the target rate and the paper currency interest rate so electronic money has an attractive return relative to paper currency.
  - Non-rate interventions (e.g., reducing cash windows) can raise electronic transactions frequency.
- Other potential ZLB sources:
  - Any government borrowing rate stuck at zero can create a ZLB; central bank must lower target rate, interest on reserves, and rates for government-paid deposits.
  - Unlimited private zero-rate funding is unlikely; assets with adjustable prices typically cannot create a ZLB.
- Legal tender considerations:
  - Legal tender inscription is symbolic; raising prestige of electronic money and lowering prestige of paper currency helps shift unit-of-account usage.
- Role of transaction share:
  - Increasing fraction of transactions in electronic form bolsters electronic money as unit of account.
  - Empirical evidence: payment card ownership rates above 80 percent in surveyed countries; cash high by transaction volume but low by transaction value; card payments dominate larger-value transactions.

### X. Responses to critiques and implementation issues (selected points 5–15)
- 5. Detailed regulations for banks and retail shops are unnecessary; banks and shops can choose any exchange rate and market forces will propagate it.
- 6. Even at modest doses, negative rates need not dramatically change daily household experience; retailers may accept cash at par until discounts become large; surcharges could be handled at the register like sales taxes.
- 7. Implementing the time-varying deposit fee requires central bank to set one more interest rate—the PCIR—alongside existing rates; otherwise compatible with standard open-market operations.
- 8. Electronic money system in “standby mode” looks much like the current system except during periods of negative rates and gradual return to par.
- 9. The overnight commitment to exchange one unit of paper currency for X units of electronic money tomorrow is likely credible; central bank must commit to keep PCIR at or slightly below the target rate.
- 10. Electronic money system does not necessarily disadvantage the unbanked; PCIR can be kept close to the target rate during negative-rate periods; eliminating ZLB could allow lowering long-run inflation target benefiting cash-reliant agents.
- 11. Deep negative rates can counteract banking dysfunction; open-economy effects and storage of physical goods can provide stimulus if rates fall far enough.
- 12. If paper currency is defanged, other sources creating a ZLB can be addressed by lowering corresponding government rates in tandem; limitations of prepaying taxes and other instruments noted.
- 13. Negative rates need not unavoidably cause financial instability; pair with higher equity requirements to protect taxpayers.
- 14. Stimulative monetary policy does not necessarily distract from supply-side reforms; ending recessions quickly can enhance credibility for reforms.
- 15. Historical precedent exists for radical monetary changes; once one central bank blazes a trail others are likely to follow.

### XI. Conclusions and key policy implications
- If electronic money provides the unit of account and inflation is close to zero in terms of the electronic unit of account, one can have inflation relative to paper currency without serious costs, provided the central bank keeps the spread between paper currency interest rate and the checking account interest rate small.
- The time-varying paper currency deposit fee:
  - Can be implemented solely by action at the cash window of the central bank.
  - Makes the paper currency interest rate an easily controlled policy variable.
  - Varying the paper currency interest rate along with other key interest rates makes it possible to stimulate investment and net exports as needed even when inflation, interest rates, and economic activity are quite low.

### XII. Appendix I — Potential steps in the transition from paper standard to electronic money
- 1. Announce technical feasibility of eliminating the zero lower bound.
- 2. Strengthen macro-prudential regulation by raising equity requirements substantially above those prescribed by Basel III.
- 3. Ask banks and other financial firms to make contingency plans for negative interest rates.
- 4. Develop accounting standards for negative interest rates that take electronic money as the unit of account, and give to paper money the value of its worth in the market relative to electronic money.
- 5. Ask government agencies to prepare contingency plans for negative interest rates and non-par valuation of paper money.
- 6. Make it clear no one has the right to pay off large debts to the government in contexts where transactions are now routinely conducted with bank money.
- 7. Establish by law that debtors do not have the right to pay off large debts with paper currency at par when the market value of paper currency is below par.
- 8. Formally make money in central-bank certified bank accounts legal tender.
- 9. Announce the intent to introduce an electronic money system.
- 10. Lower the central bank’s interest rate on reserves to zero or slightly below zero.
- 11. Lower the central bank’s target interest rate, interest rate on reserves, and the central bank’s lending rate substantially below zero.
- 12. If there is any sign of large increases in paper currency withdrawal, institute a time-varying deposit charge (levied on net deposits) when banks deposit paper currency with the central bank in exchange for reserves.
- 13. Discount vault cash applied to reserve requirements by the factor of (1-deposit charge).
- 14. Implement the accounting standards appropriate for negative interest rates and non-par valuation of paper currency.
- 15. Require payment of taxes and other substantial debts to the government in electronic form.
- 16. Implement the contingency plans for government agencies.
- 17. Ask all firms to post prices in terms of electronic money.
- 18. Make it clear that firms are allowed to specify in contracts (including loan contracts) and in retail sale the terms under which they will accept paper currency.

*Source: _wp15224 - Appendix I. Potential Steps in the Transition from Paper Standard to Electronic Money (pages indicated in source content).*

### References .............................................................................................................

### _wp15224 - References

### Section overview
- References section indicated on page: 36

*Source: _wp15224 - References (page indicator provided in source content)*

### Appendix I. Potential Steps in the Transition from Paper Standard to Electronic Money .......... 38

### Appendix I. Potential Steps in the Transition from Paper Standard to Electronic Money

### I. Introduction — problem and proposed transitional approach
- The zero lower bound (ZLB) arises because government-issued paper currency guarantees a zero nominal interest rate obtainable in unlimited quantities, creating an interest-rate floor that hinders negative nominal policy rates.
- Proposal: a transitional electronic money system in which electronic money is the unit of account while paper currency remains in circulation, combined with a time-varying paper currency deposit fee levied at the central bank’s cash window, can eliminate the option to circumvent negative rates by withdrawing, storing, and redepositing paper currency.
- Key mechanism: levy the paper currency deposit fee on net deposits at the cash window to create a time-varying exchange rate between electronic money and paper currency so paper currency can be caused to depreciate relative to electronic money when needed.
- Political and practical advantages emphasized:
  - No need for extra regulations or quantity constraints; policy works through prices.
  - Can be implemented at the central bank’s cash window within weeks.
  - Serves as a transitional system complementary to a long-run move toward a cashless economy.

### II. Using electronic money to act against paper currency storage
- Three attack points to prevent arbitrage against negative rates:
  - Attack withdrawals (restrict or fee withdrawals): disadvantages include impairing spending, destroying option value, anticipatory hoarding, and political difficulty.
  - Attack storage (tax/prohibit storage): hard to enforce because low-tech secret storage is feasible, risking disintermediation.
  - Attack redeposit (time-varying deposit fee at central bank cash window): preferred in this paper.
- Time-varying deposit fee mechanics:
  - Levied only at the cash window when private banks deposit paper currency; no new rules for bank–customer interactions required.
  - Fee on net deposits can make the bank’s effective receipt for one paper dollar equal to (1 - deposit fee) electronic dollars (ignoring transaction costs).
  - Charging the fee on net deposits makes the exchange rate two-way (discount on withdrawals and deposits), avoids banks reorganizing cash flows to net out before interacting with the cash window, and establishes a clearly defined crawling peg for the exchange rate.
- Retail pass-through considerations:
  - Many retailers currently accept different payment types at face value despite differing net receipts (e.g., credit card net receipts of 96 or 97 cents on the dollar), suggesting retailers may similarly treat discounted cash as if at par unless discounts exceed the retailers’ cost differences.
  - Up to a deposit fee of several percent, retail behavior may not change and could further encourage treating cash and card payments at par.
  - Research agenda: map retailer cash-handling costs and contractual card fees to determine when and where exchange-rate discounts would be passed through at retail.

### III. The paper currency interest rate (PCIR) and exchange rate dynamics
- Definitions and mechanism:
  - Electronic money is the numeraire; define X = number of electronic dollars per paper dollar. The PCIR is the rate of change in X: (dX/dt)/X = PCIR (as explained in text).
  - Monetary policy committees would add a fourth interest rate choice: the paper currency interest rate (PCIR), alongside target rate, interest on reserves, and lending rate. Starting at par, compound interest mechanics determine X given PCIR.
  - The deposit fee’s time path (its rate of change) is the operational instrument that creates the desired PCIR.
- Time-path options for PCIR when returning to par:
  - Swift Return to Par:
    - Rapid return to par creates a high appreciation (high PCIR) and can create a new, higher effective lower bound; anticipation would encourage preemptive paper-currency storage.
    - Considered a serious policy mistake.
  - Gradual Return to Par:
    - Keep PCIR equal to the target rate (plus/minus a small spread) until parity is reached, then set PCIR = 0.
    - Returns exchange rate to par as fast as consistent with keeping the ZLB non-binding; small spreads limit shoe-leather costs.
    - Viewed as the minimum distance from the current system.
  - Friedman Rule:
    - Keep PCIR equal to the target rate at all times (plus/minus a small spread).
    - Implies paper currency can go above par if long-run average nominal rate is positive; consistent with achieving zero inflation in the electronic unit of account without forcing deflation in that unit.
  - Seignorage without Inflation (Never Return to Par):
    - Constantly depreciate paper currency to extract seignorage while maintaining low/zero inflation in the electronic unit of account.
    - Example in text: central bank sets a constant PCIR equal to -4 percent; paper money value continues to fall relative to electronic money without creating inflation in the electronic unit of account.
- Policy commitments needed:
  - Keep PCIR at most a small spread above the target rate and interest on reserves (spread smaller than physical storage cost) to avoid large incentives for storage during policy normalization.
  - Commitment to the exchange rate one day ahead plus this PCIR behavior suffices to make negative-rate policy function smoothly.

### IV. Absence of arbitrage and the role of the time-varying exchange rate
- No-arbitrage condition:
  - Absent storage costs, absence of arbitrage requires the PCIR to be essentially equal to other short-term safe rates (interest on reserves, repo, short-term bill rates).
  - Time-varying X (exchange rate) serves like a “sundial” tracking cumulative electronic-account interest earned; the rate of change in the deposit fee (not its level) ensures parity of returns across paper and electronic holdings over time.
- Numerical/example context in the text:
  - Example trajectory: other short-term rates = -2 percent during 2009–2010, 0 percent during 2011, and +2 percent thereafter; setting PCIR equal to these short-term rates prevents arbitrage across 2009–2014.
  - Example illustration: $100 deposited in an electronic short-rate account on January 1, 2009 becomes $98, $96, $96, $98, $100, and $102 on successive New Year’s Days; paper-currency storage, converted using X, can be made to match this path through 2014 when PCIR is set accordingly.

### V. Pass-through of negative interest rates and the exchange rate
- Empirical and behavioral expectations:
  - Experience from Switzerland, Sweden, Denmark, and the eurozone (2014–15) shows negative policy rates are not immediately fully passed through to typical small household accounts.
  - Banks likely distinguish legacy customers (shield from modest negative rates) from hot-money customers (pass negative rates through).
  - Large deposits from firms and institutional investors are more likely to pay negative rates.
- Central bank strategic advantage:
  - Acting indirectly via private-firm decisions can blunt political backlash while retaining transmission.
  - Blunted pass-through at retail (shielding small account holders and some shops treating payment methods at par) is not fatal because primary transmission channels for negative rates are via asset prices, exchange rates, and purchases of investment goods and durables (usually paid electronically).
- Evidence cited:
  - Danmarks Nationalbank: its certificate-of-deposit rate has been -0.75 percent since Feb 6, 2015; negative rates did not weaken pass-through to money market rates; deposit/lending rates for households were not fully passed through, while large deposits paid negative rates; no substantial change in currency-in-circulation usage at current rates.

### VI. Impact on financial sector and contracts
- Impact on banks:
  - The spread between other short-term rates and PCIR matters for bank profitability; in current systems negative short-term rates combined with a zero paper-currency rate compress spreads and hurt profitability.
  - Electronic money system makes that spread a policy variable and can avoid compressing bank spreads unduly because depreciation mechanism still gives depositors incentive to keep funds in banks even if deposit rates are negative.
  - Banks’ customer-relations choices (shielding small accounts) may reduce pass-through and affect profits; central banks can subsidize banks to shield small accounts by linking above-market zero interest ceilings on reserve accounts to banks’ behavior in shielding households while passing negative rates to other depositors.
- Possible paths for the spread (target rate minus PCIR):
  - Case 1 (Swift Return to Par): spread may not always be positive.
  - Cases 2–4 (Gradual, Friedman, Seignorage): spread remains positive at all times in the illustrations.
  - A policy of a fixed small positive spread (e.g., a constant small spread below the target rate except when it would take paper currency above par) provides predictable communication and minimizes political salience.
- Impact on debt contracts:
  - Temporary negative rates typically raise the price of non-callable debt over horizons where rates fall, but negative rates can also have complex effects: quicker recovery may raise medium-term real rates and lower nominal bond prices; lowering long-run inflation targets can raise value of very long-term nominal bonds.
  - When paper currency is below par, borrowers might have an option to repay in cheaper paper currency unless contracts specify the unit of payment; solutions:
    - Legislate that debt contracts refer to units of electronic (bank) money.
    - Include contractual clauses specifying treatment when paper currency is away from par (legal precedent: enforceability of gold clauses suggests electronic-money clauses are enforceable).

### VII. Is breaking the ZLB desirable? Costs and benefits
- Primary benefit: removing the constraint on how low nominal interest rates can go, expanding monetary policy tools for stabilization and allowing lower long-run inflation targets without sacrificing stabilization.
- Costs associated specifically with paper currency away from par (distinct from negative rates):
  - Psychological cost: shifting the symbolic centrality of paper currency to the periphery creates political and psychological unease (salience at inception).
  - Salience mitigants: If paper currency is only a small distance from par, the average household may not notice; modest and predictable spreads reduce salience.
- Political economy point:
  - Framing the policy as a transitional move toward an eventual cashless economy can help navigate politics of reducing the central role of paper currency.

*Source: _wp15224 - Appendix I. Potential Steps in the Transition from Paper Standard to Electronic Money*

### 0.5 percent and corresponding fall in the exchange rate from 1 to .995 over the course of a

### _wp15224 - 0.5 percent and corresponding fall in the exchange rate from 1 to .995 over the course of a

### Paper currency away from par: psychological and computational costs
- Example scenario: a 0.5 percent fall in the value of paper currency with a corresponding fall in the exchange rate from 1 to .995 over the course of a year, after which the exchange rate could hold constant and perhaps later gradually appreciate from .995 back to 1.
- Psychological costs
  - Typical households may not fully perceive that the paper dollar, euro, yen or pound is no longer the unit of account because retail prices they face likely will not reflect the 0.5 percent paper-currency depreciation.
  - Displacement of paper currency from the center of the monetary system creates attachment-related queasiness.
  - This psychological cost can be alleviated by creating and fostering psychological attachment to the electronic dollar, euro, yen or pound to compete with attachment to paper currency.
- Computational costs
  - Businesses can handle a non-par exchange rate for paper currency relatively easily.
  - Households facing surcharges on certain cash purchases face complexity akin to U.S. sales taxes that are assessed at the time of final sale; such costs arise only when there is pass-through.
- Additional practical costs
  - Unintentional distortion of the meaning of preexisting debt contracts.
  - Additional transactions costs from physical transportation of paper currency if agents can make payments with below-par paper currency at face value.
- Legal or contractual mitigants
  - (1) A law interpreting monetary amounts in all contracts as referring to quantities of electronic money or the equivalent in paper money at the current exchange rate.
  - (2) Boilerplate clauses in typical debt contracts specifying how payments should be assessed whenever paper currency is away from par.
- Decentralized remedies
  - Convening legal experts and central bank legal teams could encourage insertion of contingency clauses in new debt contracts so that over a relatively short number of years most active contracts become immune to distortions from paper currency away from par.

### Benefit: taxing paper currency without inflation
- Key benefit: ability to tax paper currency separately from the inflation target of the unit of account.
- Use cases
  - If the tax system is weak in other dimensions or paper currency is associated with criminal activity or tax evasion, taxing paper currency without inducing inflation could be valuable.
  - Transitioning toward a fully cashless economy: experiment with increasing implicit taxation rates on paper currency to assess problems; if extremely high rates cause no serious problems, abolition of paper currency could be considered.

### Costs and benefits of negative interest rates
- General point: breaking the zero lower bound (ZLB) removes restraints on interest rate policy; costs and benefits must be assessed.
- Assumption note: discussion assumes a relatively responsible, independent central bank that worries about inflation being too high; different conclusions for inflation-indulgent or less independent central banks.
- Direct and indirect benefits
  - Direct: additional monetary stabilization tool via the option of negative interest rates.
  - Indirect: ability to lower the long-run inflation target by removing the need to tilt targets upward to avoid the ZLB.
- Example of conventional view influencing target choice
  - Ben Bernanke’s March 20, 2013 press conference rationale for a 2 percent inflation target: avoid proximity to deflation and ensure nominal rates are high enough to respond to recessions.
- Two-inflation perspective
  - Distinguish inflation relative to the unit of account and “inflation” relative to paper currency.
  - Allowing paper currency away from par permits the “inflation” relative to paper currency needed to avoid the ZLB without requiring inflation relative to the unit of account.
- Costs of inflation concentrated in inflation relative to the unit of account
  - Microeconomic relative price distortions from staggered price setting.
  - Menu costs (price changes).
  - Confusion costs (mistaking nominal for real rates, tax-code distortions, misleading income or inequality measures, retirement planning errors).
  - Unpredictability of prices.
  - Shoe-leather costs tied to spread between deposit rate and paper currency interest rate; central bank can choose that spread separately from the inflation target and potentially follow the Friedman rule to avoid underuse of paper currency.
- Potential benefits of inflation (four listed)
  - Greater capital taxation via nominal confusion (if beneficial).
  - Easier reductions in real wages without full worker recognition/resistance.
  - Interaction of time-discounting and Calvo reset price leading to slightly lower reset prices.
  - Positive interactions with certain financial market customs (e.g., expected speed of loan repayment linked to nominal interest rates deters Ponzi schemes).
- Policy implication on targets
  - If the optimal inflation absent the ZLB is below current targets (e.g., below 2 percent), lowering the target is unambiguously beneficial once ZLB concerns are removed.
  - Many central banks will find lowering the target hard while the ZLB remains, and raising targets risks credibility; thus breaking the ZLB could enable many central banks to choose zero target inflation.
- Communication and price-level targeting
  - Price-level targeting is easier to communicate with a zero inflation target (return to previous price level).
  - Prediction: if the ZLB is broken, many central banks may choose target inflation rates of zero.

### Other costs and dynamic considerations of negative rates
- Distinction: temporarily low interest rates vs. chronically low interest rates.
- Risk of chronically low short-term and long-term rates if an economy is trapped by a persistent output gap at the ZLB (e.g., Japan’s lost decades).
- If markets believe the ZLB has been broken and central banks will use negative rates to close output gaps, markets will anticipate higher future interest rates appropriate to a non-depressed economy.
- Model dependence
  - In models where monetary policy affects activity, adding policy tools is unambiguously good if central bank judicious.
  - In models with investment adjustment lags (Basu and Kimball, 2003) and Q-theory smoothing (Kimball, 1995; Kimball, 2014), an initial interest cut can lead to different subsequent long-run interest rates once activity adjusts; interest cuts might therefore lead to higher post-adjustment interest rates.
- Financial stability considerations
  - Low long-run rates might raise fundamental present values and potentially increase divergence from fundamentals, but if negative rates lead ultimately to higher long-run rates, they could dampen this instability channel.
  - Critiques of negative-rate policy must show not only that low rates are bad but also the dynamic path (whether cuts lead to higher future rates) and which rates matter for the claimed costs.
- Edge-case tradeoffs
  - If low long-run rates are beneficial (e.g., to maintain solvency for high-debt countries like Japan), negative short-term rates could be counterproductive by inducing a boom that raises long-run rates.

### What it takes to break through the zero lower bound
- Core claim: a specific policy can break through the ZLB; essential vs. non-essential elements are identified below.

#### A. If the government has trouble establishing electronic money as the unit of account
- Government capacity to determine the unit of account
  - Governments can influence units of account via tax rules, accounting standards, and court-adjudicated contract interpretation; pointing to a particular equilibrium can make it focal.
- If inflation expectations and inertia are anchored in terms of the electronic dollar, depreciating paper currency relative to electronic money can make the ZLB non-binding, even with a messy mix of units in use.
- Harder case: if inflation inertia is in terms of paper money, depreciating paper currency does not relieve the ZLB (though it does not worsen it).
- Central bank policy lever: make electronic accounts offer a significantly higher rate of return than paper currency to reward holding electronic balances and induce a shift of unit-of-account usage toward electronic money.
- Helicopter-drop analogy
  - From the paper-numeraire perspective, higher returns on electronic accounts act like a helicopter drop proportionate to electronic accounts; but because the central bank targets the electronic dollar as the ultimate unit of account, this stimulus need not become a long-run equilibrium helicopter drop that undermines credibility.
- Peso-to-zero example (illustration)
  - Phase 1: keep paper peso as unit of account, appreciate the electronic peso relative to paper peso at close to 7 percent per year while staying at natural output.
  - Phase 2: once expectations for electronic peso inflation anchor near zero, encourage firms and households to set prices and accounts in electronic money.
  - If credibility about staying at natural output is met, such a program could lower inflation from 7 percent per year to zero without larger output deviations than a steady 7 percent inflation path would have caused.
- Empirical note: past currency reforms indicate governments often can engineer shifts in unit of account; making ambiguous unit of account (par between paper and electronic) into an electronic standard should be easier for low-inflation inheriting governments.

#### B. Avoiding “paperization” when using negative rates without lowering paper-currency interest below zero
- Risk: prolonged zero or negative target rates with paper currency at par can encourage greater use of paper currency—“paperization” (e.g., Japan and Germany).
- To avoid paperization, central bank can choose a large enough spread between the target rate and the paper currency interest rate so electronic money has an attractive return relative to paper currency.
- Policy flexibility: widen the interest-rate spread for electronic money over paper currency only if signs of paperization appear; adjust in a data-dependent way.
- Non-rate interventions: increasing costs of handling paper currency (e.g., reducing cash windows as Sweden did) can raise electronic transactions frequency and counteract paperization; but changing handling costs affects pass-through of exchange rates for paper currency.

#### C. Other potential sources of a zero lower bound
- Any government borrowing rate stuck at zero can create a ZLB; thus central bank must lower target rate, interest on reserves, and rates for government-paid deposits.
- Example: between-tax-year interest on excess tax payments (current U.S. law sets the between-tax-year interest rate by the Secretary of the Treasury in line with other short-term rates; the interest rate is zero within a tax year).
- Any unlimited private lending option to government must also have rates lowered.
- Private agents rarely create a ZLB because providing unlimited zero-rate funding requires very deep pockets and disregard for profit.
- Test: assets whose prices can adjust typically cannot create a ZLB because returns change via price adjustments; risk-free arbitrage via paper currency arises due to commitment to keep paper currency at par.

#### D. Legal tender considerations
- Debt contracts are fungible: face value is not market value; preexisting debt contracts cannot clone a ZLB.
- Legal tender inscription still matters symbolically: calling paper currency legal tender can signal it as unit of account to those unaware of technical distinctions.
- Raising prestige of electronic money and lowering prestige of paper currency can help shift unit-of-account usage; naming policy “electronic money” helps.

#### E. Role of transaction share in bolstering electronic money as unit of account
- Increasing fraction of transactions in electronic form (cards, transfers, checks) helps demote paper currency.
- Trends that rebate transaction fees to card users can raise electronic transaction share.
- Innovations reducing transaction fees (disrupting card oligopoly) could further encourage card use.
- Empirical evidence (Bagnall et al., 2014, survey 2009–2012)
  - Cash usage remains high by transaction volume but low by transaction value in advanced countries.
  - Card payments dominate larger-value transactions; cash is mainly used for smaller transactions.
  - Payment card ownership rates above 80 percent in surveyed countries suggest rapid increases in electronic transactions are feasible with small-transaction payment innovations.

### Misconceptions about eliminating the zero lower bound (selected)
- Misconception 1: “Eliminating the zero lower bound is unnecessary”
  - Counterpoints:
    - Fiscal policy and quantitative easing have limitations: fiscal policy raises national debt and lacks technocratic institutions comparable to central banks; quantitative easing was not used in sufficiently large doses and lacks robust theoretical understanding.
    - Historical experiences (e.g., Japan) and recent advanced-country episodes show existing tools often fail to produce quick recoveries.
- Misconception 2: “Policymakers can’t do anything about the zero lower bound”
  - Reality: the ZLB is a policy choice, not an immutable law.
- Misconception 3: “Eliminating the zero lower bound requires abolishing paper currency or physically altering each bill”
  - Reality: attacking incentives for large-scale paper-currency storage can eliminate the ZLB without physical alteration.
- Misconception 4: “Eliminating the zero lower bound requires making storage illegal, making paper currency scarce, or restricting withdrawals”
  - Reality: under the time-varying deposit fee mechanism, an effective exchange rate between paper currency and reserves exists with unrestricted exchange and no storage/withdrawal restrictions; deposit fee applies between central bank and private banks only.

*Italicized source: _wp15224 - 0.5 percent and corresponding fall in the exchange rate from 1 to .995 over the course of a (PDF chapter/section).*

### Section II.B and II.C above).

### _wp15224 - Section II.B and II.C above)

### Responses to critiques and implementation issues (points 5–15)
- 5. “Detailed regulations for banks and retail shops would be needed to eliminate zero lower bound”:
  - Banks and shops can and should be allowed to choose any exchange rate they choose.
  - Market forces will cause the exchange rate between paper currency and electronic money (i.e., reserves or bank money) to hold throughout the banking and financial system (see Section II.B and II.C above).
  - Retail shops would in practice have leeway in their exchange rate pass-through decisions.

- 6. “Even at modest doses, negative interest rates will dramatically change the daily experience of regular households.”:
  - Despite paying 2 percent to 4 percent in credit card and debit card fees, retail shops often charge the same for cash and for credit/debt transactions; retailers may accept paper currency at par even if paper currency is running up to 4 percent or 5 percent below par.
  - If paper currency went deeper below par, cash surcharges would be likely to be implemented by retailers gradually, with some stores moving before others.
  - These surcharges could be handled at the register much the same way sales taxes are now, but only on cash purchases.

- 7. “Implementing the time-varying deposit fee requires a totally new way of thinking about monetary policy”:
  - Implementation essentially requires the central bank to set one more interest rate at regular meetings—the paper currency interest rate—in addition to the target rate, interest on reserves and lending rate.
  - This does not require any other change to implementation of monetary policy, and in fact may simplify monetary policy since it removes the need for quantitative easing or forward guidance for stabilization.
  - Breaking through the zero lower bound is fully compatible with using open market purchases and sales of short-term Treasury bills as the central tool of monetary policy.
  - A negative Treasury bill rate corresponds to a price for a Treasury bill above the principal returned at maturity.
  - The time-varying effective exchange rate between paper currency and electronic money at the cash window of the central bank is a way to get paper currency out of the way—analogous to cutting interest on reserves when cutting the target rate.

- 8. “The electronic money system involves significant costs even in ‘standby mode’ when there is no need for negative interest rates”:
  - Except during the period of negative interest rates and a period of gradual return to par thereafter, the electronic money system looks much like the current system (see Section II.C).
  - When negative interest rates are no longer needed paper currency can be at par again with electronic currency, like in the current system.

- 9. “An electronic money system requires a stronger ability to commit than regular monetary policy”:
  - The paper currency interest rate is given by an overnight commitment to exchange one unit of paper currency for X units of electronic money tomorrow; such an overnight commitment is likely to be fully credible.
  - The central bank needs to commit to keep the paper currency interest rate at or slightly below the target rate to avoid problems; this is credible since it is disruptive to have the paper currency interest rate far above other rates.
  - The remaining commitment problem—avoiding overheating the economy by keeping rates too low—is the same commitment problem faced by central banks in the current system.

- 10. “An electronic money system disadvantages cash and the unbanked”:
  - Not true in general: during periods of negative rates, the paper currency interest rate can be kept very close to the target rate, thereby having no differential impact on the unbanked (one exception discussed in Section V.A).
  - Eliminating the zero lower bound would likely allow a reduction in the long run inflation target, which would benefit those who rely on the cash economy.
  - The central bank could follow the Friedman rule regardless of inflation rate if it is willing to let paper currency go above par (see Section II.C).

- 11. “Deep negative rates are not enough if the banks are messed up as they were during the Great Recession”:
  - Any finite risk or liquidity premium can be countervailed by deep enough negative rates; housing construction will kick in at some point.
  - Open-economy effects can stimulate exports through the international capital flow/exchange rate channel.
  - In extreme cases, storage of physical goods can provide needed stimulus to return to the natural level of output if interest rates fall far enough.

- 12. “Even if paper currency is defanged, other things would generate a zero lower bound”:
  - As long as the paper currency interest rate and all other government borrowing rates go negative in tandem, nothing else will stop negative interest rates from going into deep enough negative territory.
  - Private firms are unlikely to offer zero interest rates when market interest rates are deep in negative territory.
  - Any asset whose price can fluctuate can rise enough in price under negative interest rates to have a return low enough to be consistent with negative safe rates (applies to preexisting debt contracts, foreign currency, gold, or even preexisting gift cards redeemable at par including those redeemable for an electronic refund at par).
  - The ability to get a zero interest rate through the tax system is limited to prepaying within the tax year; the value of this prepayment option is limited in present value to avoiding roughly half a year’s negative interest on a typical year’s tax liability (unless income tends to come especially late in the tax year).
  - Forever postage stamps, despite a built-in zero real interest rate, have not generated a zero real lower bound because they cannot be turned in for a refund in unlimited quantities and issuance could cease at any time.

- 13. “Negative rates would unavoidably cause financial instability”:
  - Even if low interest rates are detrimental to financial stability, temporarily negative interest rates could actually help by raising long-term rates.
  - Important to pair negative interest rates with progressively higher equity (capital) requirements in the form of high capital conservation buffers to ensure business mistakes are borne by banks/firms and not taxpayers.
  - The stimulative power of negative interest rates on tap makes it unnecessary to get extra aggregate demand by allowing financial bubbles; thus there is no aggregate demand reason not to pursue higher equity requirements for banks if the zero lower bound is eliminated.

- 14. “Stimulative monetary policy distracts from supply-side reforms”:
  - Although logically possible, there are reasons to doubt stimulative monetary policy distracts from supply-side reforms under current circumstances.
  - Knowledge that more demand-side stimulus is needed can distract from supply-side reforms at least as much as having stimulative monetary policy.
  - Many supply-side reforms require reallocation of labor and capital—something that typically looks too painful to insist on in a recession when unemployment is high.
  - Governments that end recessions quickly gain the credibility to implement tough reforms.
  - Monetary stimulus avoids the increase in national debt that can distract from or directly interfere with supply-side reform.

- 15. “It will never happen”:
  - Something of equivalent magnitude happened in the twentieth century: the end of the gold standard.
  - The experience of quantitative easing shows central banks can implement policies previously seen as radical.
  - Politics differ by country, but once one central bank blazes the trail, others are more likely to follow; international capital flow/exchange rate effects for early adopters will encourage others to break through the zero lower bound.

### Conclusions (VII)
- Eliminating the zero lower bound has some costs, but those costs should be weighed against benefits: ending recessions and ending inflation.
- Key analytical point:
  - if electronic money provides the unit of account (including the unit of account for price and wage setting),
  - and inflation is close to zero in terms of the electronic unit of account,
  - then one can have inflation relative to paper currency without serious costs,
  - as long as the central bank keeps the spread between the paper currency interest rate and the checking account interest rate small.
- The time-varying paper currency deposit fee:
  - Can be implemented solely by action at the cash window of the central bank.
  - The effective exchange rate between paper currency and electronic money at the cash window makes the paper currency interest rate an easily controlled policy variable of the central bank.
  - Varying the paper currency interest rate along with other key interest rates (which can be modified by standard means, even in negative territory) makes it possible to stimulate investment and net exports as much as needed to revive the economy, even when inflation, interest rates, and economic activity are quite low.

### Appendix I — Potential steps in the transition from paper standard to electronic money
- 1. Announce technical feasibility of eliminating the zero lower bound.
- 2. Strengthen macro-prudential regulation by raising equity requirements substantially above those prescribed by Basel III.
- 3. Ask banks and other financial firms to make contingency plans for negative interest rates.
- 4. Develop accounting standards for negative interest rates that take electronic money as the unit of account, and give to paper money the value of its worth in the market relative to electronic money.
- 5. Ask government agencies to prepare contingency plans for negative interest rates and non-par valuation of paper money.
- 6. Make it clear no one has the right to pay off large debts to the government in contexts where transactions are now routinely conducted with bank money.
- 7. Establish by law that debtors do not have the right to pay off large debts with paper currency at par when the market value of paper currency is below par.
- 8. Formally make money in central-bank certified bank accounts legal tender.
- 9. Announce the intent to introduce an electronic money system.
- 10. Lower the central bank’s interest rate on reserves to zero or slightly below zero.
- 11. Lower the central bank’s target interest rate, interest rate on reserves, and the central bank’s lending rate substantially below zero.
- 12. If there is any sign of large increases in paper currency withdrawal, institute a time-varying deposit charge (levied on net deposits) when banks deposit paper currency with the central bank in exchange for reserves.
- 13. Discount vault cash applied to reserve requirements by the factor of (1-deposit charge).
- 14. Implement the accounting standards appropriate for negative interest rates and non-par valuation of paper currency.
- 15. Require payment of taxes and other substantial debts to the government in electronic form.
- 16. Implement the contingency plans for government agencies.
- 17. Ask all firms to post prices in terms of electronic money.
- 18. Make it clear that firms are allowed to specify in contracts (including loan contracts) and in retail sale the terms under which they will accept paper currency.

*Source: _wp15224 - Section II.B and II.C above).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15224.pdf_